The crew immediately apprise Captain Needa of the situation and tell him they will continue searching.
Well, the crew tells him that there is no trace and that Vader demands an update on the pursuit.
NEEDA
They can't have disappeared. No ship that small has a cloaking device.TRACKING OFFICER
Well, there's no trace of them, sir.COMMUNICATIONS OFFICER
Captain, Lord Vader demands an update on the pursuit.NEEDA
(drawing a breath) Get a shuttle ready. I shall assume full responsibility for losing them, and apologize to Lord Vader. Meanwhile, continue to scan the area.
So it's Needa himself who instructs the crew to keep searching. He's just been told that there's no trace of them. He could stay there and drag it out, hoping to find the ship. However, Darth Vader has demanded an update. I have a feeling that Lord Vader is not the kind of guy you let wait. When he calls you, you respond instantly. Needa may feel that if he goes like a man and admits his mistake, he might have a chance, but if he makes Vader wait, he's sure to be killed. He may fear that the Falcon is lost, so if he makes Vader wait and then gives the exact same news, it will mean certain death for him. So he might as well go immediately.